Fringed by snow-capped mountains and buffered with thick swathes of forest, Seattle is a place where urban sprawl is tempered by ocean and sky.

A carnival of big wheels and bright lights, the port hosts gargantuan cruise ships departing for Alaska. But once their hulking shadows have melted into the horizon, Washington state’s largest city begins to shine.

After dark, bulbs flicker on neon signage hanging from the Paramount Theatre where Nirvana gave birth to grunge, and queues of gig-goers crowding pavements prove the scent of Kurt Cobain’s teen spirit lingers on.

But nothing smells stronger than the heart-racing aroma of brewed coffee wafting from open windows and steaming take-out cups. Starbucks has since proliferated worldwide to become something Seattle is not: An epitome of identikit chain culture. But the company’s heritage resonates through whirring espresso machines in indie cafes, and the original 1971 store is still a bastion of caffeine kicks.

Follow the crowds to find it at Pike Place Market, one of America’s oldest continuously running farmers’ markets in operation since 1907.

Further along the waterfront, cranes and architects with clipboards are busy revitalising the area surrounding historic Pioneer Square, while Downtown buildings once left languishing in their own dust and rubble have been reincarnated as trendy hotels.

The boom? It’s partly down to tech giants like Amazon and Google, who some might say have colonised the city. But despite their corporate presence, a bohemian spirit still flows through neighbourhoods like Ballard and Fremont, where fairy-tale sculptures huddle below bridges and dinosaur topiary decorates sidewalks.

From the hirsute silhouette of a Sasquatch presiding over comic book stores, to the brilliant tip of Mount Rainier visible on a clear day, the wilds of the Pacific Northwest still influence this Emerald City. It’s an urban centre for people who aren’t really urban, and a progressive hub with a reverence for the past.

In short, Seattle is a destination for anyone who likes to switch between concrete edifices and skyscrapers sprouting evergreen leaves - a city refusing to be a city in any conventional sense.

Watch whales in the Puget Sound

From acrobatic humpbacks to barnacle-nosed grays, an array of cetaceans can be seen in the waters which run from Seattle up to Vancouver Island on the Canadian border. The biggest draw of them all, however, is the orca. Both resident and transient pods are regularly seen on whale watching tours departing from the Port of Edmonds (about a 40-minute drive from Downtown).

How: Puget Sound Express (pugetsoundexpress.com) operate half-day tours between April and December, from $135/£111.

Sleep in an iconic piece of architecture

Built in 1904, the redbrick building on Second and Pike Street had several incarnations before it’s recent opening as The State Hotel. Once a dentist’S and a drug store, it was abandoned in the 1940s, and now offers one of the city’s finest sleeps.

Inspired by markets, seafood and street performers, custom-made wallpaper by local artist Kate Blairstone decorates each floor, while a curious collage of doorknobs collected from across the state dominates the buzzy reception lounge.

On the top floor, a slither of roof terrace boasts the best views you can possibly get of Pike Place Market.

How: Doubles, room only, from $195/£160 per night. Visit statehotel.com.

Sip coffee in Fremont

Of all the neighbourhoods fanning from Downtown, Fremont has the quirkiest appeal. Artists have left their mark in various street furnishings: Look out for a Cold War rocket perched on top of a building, pose with a family of aluminium figures at a bus stop, or stumble upon the centre of the universe where a signpost lists distances to destinations across the globe.

You can relax in wicker chairs on the veranda of Fremont Coffee Company (459N 36th St), where baristas channelling Kurt Cobain sport an equally dishevelled look.

Climb to the top of the Space Needle

Replicated on badges, magnets and T-shirts, this observation tower has become an icon of Seattle. Erected in 1962 for the Century 21 Exposition, its design was inspired by Space Age exploration. A recent multi-million-dollar renovation gave the tower a facelift, creating the world’s first rotating glass floor in lower observation level, The Loupe, and adding angled glass windows to the upper level for improved views.

How: Entry from $32.50/£27. Visit spaceneedle.com.

Getting there:

Norwegian (norwegian.com/uk; 0330 8280854) offers affordable flights to Seattle from London Gatwick on modern Boeing 787 Dreamliner aircraft that feature a Premium cabin. Economy fares start from £294.80 return and £1,109.80 return in Premium